How do you find the angles of a right triangle

Asked by admin @ 07/11/2021 in Mathematics viewed by 322 People

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

Answered by admin @ 07/11/2021

Step-by-step explanation:

STEP 1:

Find a length of third side.

Use the Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

STEP 2:

Use the trigonometric functions:

$sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}\\\\tangent=\dfrac{opposite}{adjacent}$

STEP 3:

Use theorem: the sum of the measures of acute angles of the right triangle is 90°.

Example:

We have the length of legs: a = 3, b = 4.

Let c = hypotenuse.

Use the Pyhagorean theorem:

$c^2=3^2+4^2\\\\c^2=9+16\\\\c^2=25\to c=\sqrt{25}\\\\c=5$

Angle between a and c (β):

Use sine. Therefore b = opposite, c = hypotenuse:

$\sin\beta=\dfrac{4}{5}=0.8$

look at the picture

$\beta\approx37^o$

$\alpha+\beta=90^o\to\alpha+37^o=90^o$ subtract 37° from both sides

$\alpha=53^o$

How to find angle in right triangle with 3 sides

Asked by admin @ 05/11/2021 in Mathematics viewed by 374 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

How to find sides and angles of a right triangle

Asked by admin @ 29/10/2021 in Mathematics viewed by 336 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

How to find the base of a right angled triangle

Asked by admin @ 04/08/2021 in Math viewed by 310 persons

Formula of finding base of right angled triangle

How to find the missing angle of a right triangle

Asked by admin @ 27/11/2021 in Mathematics viewed by 291 persons

How do you solve for a missing angle of theta in a right triangle?

How to find length of right triangle with only angles

Asked by admin @ 26/11/2021 in Mathematics viewed by 279 persons

How to find the length of a triangle with only one side non right triangle?

Find the missing angle of a right triangle using trigonometry

Asked by admin @ 22/11/2021 in Mathematics viewed by 308 persons

How do I find the missing sides of this triangle by using trigonometry I dont know if I did this right

How to find the hypotenuse of a right angle triangle

Asked by admin @ 03/11/2021 in Mathematics viewed by 310 persons

To solve for the hypotenuse of a right triangle, what information do you need? A. just the measure of one of the acute angles and the length of one side …

Can we have a triangle with two right angles

Asked by admin @ 23/08/2021 in Math viewed by 393 persons

Can you draw a triangle with two right angles? Give reasons.

Can you have a triangle with two right angles

Asked by admin @ 12/08/2021 in Math viewed by 318 persons

Can you draw a triangle with two right angles? Give reasons.

How do you find the missing angle of a triangle

Asked by admin @ 22/11/2021 in Mathematics viewed by 350 persons

First determine the missing angle for triangle 1 and triangle 2. Then apply the angle-angle criterion to determine if the two triangles are similar. Choose all that are similar. Triangle …