Triangle P Q R is shown. Angle Q P R is a right angle. The length of hypotenuse Q R is 14.1 and the length of P R is 12.7.
What is the measure of ∠R in △PQR? Round to the nearest degree.

26°
42°
45°
64°

∠ R ≈ 26°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos R = = = , thus

R = ( ) ≈ 26° ( to the nearest degree )

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: