How to find angle in right triangle with 3 sides

Asked by admin @ 05/11/2021 in Mathematics viewed by 368 People

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

Answered by admin @ 05/11/2021

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

$\alpha=53^o$

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