Question

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

Answer 1

K=43° to the nearest degree

Step-by-step explanation

Use the sine rule:

`( \sin(J) )/(j) = ( \sin(L))/(l)`

Substitute the values

`( \sin(J) )/(10) = ( \sin(102 \degree))/(17)`

This gives us,

`\sin(J) = ( \sin(102 \degree))/(17) * 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`