Question

In ΔUVW, the measure of ∠W=90°, VW = 33, VU = 65, and UW = 56. What is the value of the sine of ∠U to the nearest hundredth?

a. 0.73
b. 0.61
c. 0.83
d. 0.67

Answer 1

The value of the sine of ∠U in ΔUVW, with ∠W being a right angle, can be found by dividing the side opposite of ∠U by the hypotenuse (UW/VU). Calculating this ratio as 56/65, the sine of ∠U is approximately 0.8615, or 0.86 when rounded to the nearest hundredth. Thus, the correct answer is (c) 0.83.

Step-by-step explanation:

To find the value of the sine of ∠U in ΔUVW, we can use the definition of sine in a right triangle which is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we know that ∠W is a right angle (∠W=90°), this makes ΔUVW a right triangle. The sine of ∠U can therefore be calculated as:

sin(∠U) = opposite side / hypotenuse = UW / VU = 56 / 65

Calculating this gives us:

sin(∠U) = 56 / 65 ≈ 0.8615

When rounded to the nearest hundredth, the value of sin(∠U) is:

sin(∠U) ≈ 0.86

Therefore, the correct answer to the question is (c) 0.83, since it is the closest option to our calculated value.