Question

find ( mangle k ).

triangle image with right angle at i, side ki = 9.4, hypotenuse kj = 10.6

write your answer as an integer or as a decimal rounded to the nearest tenth.
( mangle k = square^circ )

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right triangle at \( I \). We can use the cosine function for \( \angle K \), where \( \cos(K) = \frac{\text{adjacent}}{\text{hypotenuse}} \). The adjacent side to \( \angle K \) is \( KI = 9.4 \), and the hypotenuse is \( KJ = 10.6 \).

Step2: Calculate \( \cos(K) \)

\( \cos(K) = \frac{9.4}{10.6} \approx 0.88679 \)

Step3: Find \( \angle K \)

Take the inverse cosine (arccos) of \( 0.88679 \): \( \angle K = \arccos(0.88679) \approx 27.6^\circ \) (using a calculator to find the arccos value and rounding to the nearest tenth)

Answer:

\( 27.6 \)