Question

Consider the following information:

Angles P and Q are complementary angles.
sin(P) = 0.6
sin(Q) = 0.8
What is the value of tan(Q)? Round your answer to the hundredths place.

A. 0.67
B. 0.75
C. 1.25
D. 1.43

Answer 1

To find the value of tan(Q), we need to determine the measures of angles P and Q. By using the complementary property of the angles and the given sine values, we can find the measure of angle P and then substitute it to find the measure of angle Q. Finally, we can calculate tan(Q) using the sine and cosine functions.

Step-by-step explanation:

Given that angles P and Q are complementary, we know that the sum of their measures is 90 degrees.

Since sin(P) = 0.6, we can find the measure of angle P using the inverse sine function: P = sin^-1(0.6).

Substituting the value of angle P in the equation sin(Q) = 0.8, we can find the measure of angle Q: sin(Q) = sin(90 - P).

Now, we can find the value of tan(Q) using the sine and cosine functions: tan(Q) = sin(Q) / cos(Q).

Therefore, the value of tan(Q) is 1.43 (D) when rounded to the hundredth place.