What kind of calculator do I need for trigonometry?

Calculators needed for my classes. WHAT KIND OF CALCULATOR DO I NEED FOR YOUR CLASS? For College Algebra, Trigonometry, Precalculus Algebra & Trigonometry, Geometry for Education, Calculus I and Calculus II: A scientific calculator .

How do you find the answer to a right triangle?

The Pythagorean Theorem gives us a 2 + b 2 = c 2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so b 2 = 14 2 – 5 2 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

Does 30 40 50 make a right triangle?

Consequently, if we are given these three side lengths we know it refers to a right triangle. Additionally, all multiples are also right triangles . For example, 30:40:50 or 6:8:10 are both multiples of 3:4:5 and both indicate right triangle measurements.

Is it possible to do trigonometry without a calculator?

Evaluating Trigonometric Functions without a Calculator For trigonometric functions of Graphical Axes, you can easily solve the problems using the easy-to-remember patterns for 0°, 90°, 180°, and 270° . The values of Sine and Cosine for these angles are quite easy to be saved in your memory.

What setting should my calculator be on for trigonometry?

What setting should my calculator be on trigonometry? You need to have access to the sine, cosine, tangent functions of trigonometry . So if your calculator has a mode where these are not present you need to put it in “scientific mode” to make them present.

How to solve right triangles easily?

Solving right triangles We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle , that is, to find unknown parts in terms of known parts. Pythagorean theorem: a 2 + b 2 = c 2 . Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

What does Soh Cah toa?

The mnemonic SOHCAHTOA can be used to aid in remembering which function to use in what circ*mstance - SOH stands for Sine is opposite over hypotenuse; CAH stands for Cosine is adjacent over hypotenuse; and TOA stands for Tangent is opposite over adjacent . This will save confusion when working with these functions.

How is right triangle trigonometry used in real life?

Trigonometry is used in navigating directions ; it estimates in what direction to place the compass to get a straight direction. With the help of a compass and trigonometric functions in navigation, it will be easy to pinpoint a location and also to find distance as well to see the horizon.

Does 5 12 13 make a right triangle?

Yes, 5 12 and 13 make a right triangle . They are referred to as Pythagorean triplets, where 5 squared and 12 squared equal 13 squared, which is the application of the Pythagorean theorem.

What is the 3/4/5 rule?

To get a perfectly square corner, you want to aim for a measurement ratio of 3:4:5. In other words, you want a three-foot length on your straight line, a four-foot length on your perpendicular line, and a five-foot length across . If all three measurements are correct, you'll have a perfectly square corner.

Can 4 5 6 make a right triangle?

Hence, 4,5 and 6 cannot form the sides of right angled triangle .

What is the 3 4 5 triangle rule?

What is the 3-4-5 triangle rule? The 3-4-5 triangle rules states if a triangle has the constant ratio 3:4:5 as its side lengths, then the triangle is a right triangle . The 3-4-5 triangle satisfies the Pythagorean Theorem which uses the sides lengths of a triangle to prove it is a right triangle.

What calculator do you need for algebra 2 trig?

CATIGA Scientific Calculator 2 Line - for Math (Algebra and Trigonometry), Science, Statistics, Engineering, Physics, Business Class, Over 200 Functions, with Memory and Replay Function.

Right Triangle Trigonometry Calculator (2024)

Created by Davide Borchia

Reviewed by

Luis Hoyos

Last updated:

Jan 26, 2024

Table of contents:

Basics of trigonometry
Right triangles trigonometry calculations
Example of right triangle trigonometry calculations with steps
More trigonometry and right triangles calculators (and not only)
FAQ

The right triangle trigonometry calculator can help you with problems where angles and triangles meet: keep reading to find out:

The basics of trigonometry;
How to calculate a right triangle with trigonometry;
A worked example of how to use trigonometry to calculate a right triangle with steps;

And much more!

Basics of trigonometry

Trigonometry is a branch of mathematics that relates angles to the length of specific segments. We identify multiple trigonometric functions: sine, cosine, and tangent, for example. They all take an angle as their argument, returning the measure of a length associated with the angle itself. Using a trigonometric circle, we can identify some of the trigonometric functions and their relationship with angles.

Right Triangle Trigonometry Calculator (1)

As you can see from the picture, sine and cosine equal the projection of the radius on the axis, while the tangent lies outside the circle. If you look closely, you can identify a right triangle using the elements we introduced above: let's discover the relationship between trigonometric functions and this shape.

Right triangles trigonometry calculations

Consider an acute angle in the trigonometric circle above: notice how you can build a right triangle where:

The radius is the hypotenuse; and
The sine and cosine are the catheti of the triangle.

$\alpha$ α is one of the acute angles, while the right angle lies at the intersection of the catheti (sine and cosine)

Let this sink in for a moment: the length of the cathetus opposite from the angle $\alpha$ α is its sine, $\sin(\alpha)$ sin(α)! You just found an easy and quick way to calculate the angles and sides of a right triangle using trigonometry.

The complete relationships between angles and sides of a right triangle need to contain a scaling factor, usually the radius (the hypotenuse). Identify the opposite and adjacent. We can then write:

$\begin{split}\sin(\alpha)&= \frac{\mathrm{opposite}}{\mathrm{hypotenuse}}\\[1em]\cos(\alpha)&= \frac{\mathrm{adjacent}}{\mathrm{hypotenuse}}\\[1em]\tan(\alpha)&= \frac{\mathrm{opposite}}{\mathrm{adjacent}}\\[1em]\end{split}$ sin(α)cos(α)tan(α)=hypotenuseopposite=hypotenuseadjacent=adjacentopposite

By switching the roles of the legs, you can find the values of the trigonometric functions for the other angle.

Taking the inverse of the trigonometric functions, you can find the values of the acute angles in any right triangle.

Using the three equations above and a combination of sides, angles, or other quantities, you can solve any right triangle. The cases we implemented in our calculator are:

Solving the triangle knowing two sides;
Solving the triangle knowing one angle and one side; and
Solving the triangle knowing the area and one side.

Example of right triangle trigonometry calculations with steps

Take a right triangle with hypotenuse $c = 5$ c=5 and an angle $\alpha=38\degree$ α=38°. Surprisingly enough, this is enough data to fully solve the right triangle! Follow these steps:

Calculate the third angle: $\beta = 90\degree - \alpha$ β=90°−α.
Calculate the sine of $\alpha$ α and use its value to find the length of the opposite cathetus:
- $\sin(\alpha) = 0.61567$ sin(α)=0.61567.
- $\mathrm{opposite} = \sin(\alpha)\cdot\mathrm{hypotenuse} = 0.61567 \cdot 5 = 3.078$ opposite=sin(α)⋅hypotenuse=0.61567⋅5=3.078.
Find the length of the last side by either using Pythagoras' theorem or the cosine relations $\cos(\alpha) = \mathrm{adjacent}/\mathrm{hypotenuse}$ cos(α)=adjacent/hypotenuse. Given $\cos(\alpha) =0.788$ cos(α)=0.788:
- $\mathrm{adjacent} = 0.788\cdot 5 = 3.94$ adjacent=0.788⋅5=3.94.

That's it!

More trigonometry and right triangles calculators (and not only)

If you liked our right triangle trigonometry calculator, why not try our other related tools? Here they are:

The trigonometry calculator;
The cosine triangle calculator;
The sine triangle calculator;
The trig triangle calculator;
The trig calculator;
The sine cosine tangent calculator;
The tangent ratio calculator; and
The tangent angle calculator.

FAQ

How do I apply trigonometry to a right triangle?

To apply trigonometry to a right triangle, remember that sine and cosine correspond to the legs of a right triangle. To solve a right triangle using trigonometry:

Identify an acute angle in the triangle α. For this angle:
- sin(α) = opposite/hypotenuse; and
- cos(α) = adjacent/hypotenuse.
By taking the inverse trigonometric functions, we can find the value of the angle α.
You can repeat the procedure for the other angle.

What is the hypotenuse of a triangle with α = 30° and opposite leg a = 3?

The length of the hypotenuse is 6. To find this result:

Calculate the sine of α: sin(α) = sin(30°) = 1/2.
Apply the following formula:
sin(α) = opposite/hypotenuse
hypotenuse = opposite/sin(α) = 3 · 2 = 6.

That's it!

Can I apply right-triangle trigonometric rules in a non-right triangle?

Not directly: to apply the relationships between trigonometric functions and sides of a triangle, divide the shape alongside one of the heights lying inside it. This way, you can split the triangle into two right triangles and, with the right combination of data, solve it!