Question

a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.

Answer 1

Check the picture below.

`\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y`

Make sure your calculator is in Degree mode.

Answer 2

• 4.31 in
• 5.52 in

Explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

Trig functions

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse×Sin

Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse×Cos

Application

The given triangle will have opposite and adjacent sides of ...

opposite = (7 in)sin(38°) ≈ 4.31 in

adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.