In right triangle JKL, the measure of angle K is 90^\circ. If \cos(J) = 0.28, what is the … — SAT

In right triangle $JKL$ , the measure of angle $K$ is $90^\circ$ . If $\cos(J) = 0.28$ , what is the value of $\sin(L)$ ?

Answer: 0.28

The correct answer is 0.28 (or the equivalent fraction 7/25).

In a right triangle, the two acute angles are complementary, meaning they add up to

90^\circ

. The co-function identity states that the sine of an acute angle is equal to the cosine of its complement. Therefore, in right triangle

JKL

with right angle

K

\sin(L) = \cos(J)

. Given that

\cos(J) = 0.28

, the value of

\sin(L)

must also be

0.28

Determine the relationship between angles

J

and

L

J + L = 90^\circ

Since the sum of angles in a triangle is

180^\circ

and angle

K

90^\circ

, the sum of the remaining two angles must be

180^\circ - 90^\circ = 90^\circ

Use the co-function trigonometric identity.

\sin(L) = \cos(J)

The sine of an acute angle in a right triangle is equal to the cosine of its complementary angle.

Substitute the given value of

\cos(J)

into the identity.

\sin(L) = 0.28

We are given that

\cos(J) = 0.28

Complementary angle trigonometric identity (co-function identity)

Question