Question

In Δvwx, the measure of ∠x is 90°, vx is 45, wv is 53, and xw is 28. What is the value of the tangent of ∠v to the nearest hundredth?

Answer 1

To find the tangent of ∠v in triangle vwx, first use the Pythagorean theorem to find the length of side wx, then divide the opposite side by the adjacent side to find the tangent.

Step-by-step explanation:

To find the value of the tangent of ∠v, we need to determine the ratio of the length of the side opposite ∠v to the length of the side adjacent to ∠v in triangle vwx.

Given that ∠x is the right angle (∠x = 90°), vx = 45, wv = 53, and xw = 28, we can use the Pythagorean theorem to find the length of side wx:

1. Use the Pythagorean theorem: wx² = wv² - vx². Substituting the values, we get wx² = 53² - 45².
2. Calculate wx by taking the square root of both sides: wx = √(53² - 45²).

Now that we have the lengths of the side opposite (√(53² - 45²)) and the side adjacent (28) to ∠v, we can find the tangent by dividing the opposite side by the adjacent side: tan(∠v) = (√(53² - 45²)) / 28.

Calculating this value will give you the tangent of ∠v to the nearest hundredth.