Question

Help! What is the measure of angle K in the triangle below?

Answer 1

ANSWER

K=43° to the nearest degree

EXPLANATION

Use the sine rule:

$\frac{ \sin(J) }{j} = \frac{ \sin(L)}{l}$

Substitute the values

$\frac{ \sin(J) }{10} = \frac{ \sin(102 \degree)}{17}$

This gives us,

$\sin(J) = \frac{ \sin(102 \degree)}{17} \times 10$

$J = \sin ^{ - 1} (0.57538094161) = 35.126 \degree$

J is approximately 35°

We now use the sum of interior angles of a triangle to find K.

$K + 35 \degree + 102 \degree = 180 \degree$

$K = 180 \degree - 35 \degree - 102 \degree$

$K = 43 \degree$