How to figure out an angle of a right triangle

Asked by admin @ in Mathematics viewed by 269 People

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

Answered by admin @


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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