Question

find the value of tan u rounded to the nearest hundredth, if necessary.
triangle with right angle at v, wv=15, wu=25, vertices w, v, u
answer attempt 1 out of 2
tan u = input box submit answer

Explanation:

Step1: Find the length of VU

In right triangle \( VUW \), we know the hypotenuse \( WU = 25 \) and one leg \( WV = 15 \). Using the Pythagorean theorem \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse and \( a, b \) are the legs. Let \( VU = x \), then \( 15^2 + x^2 = 25^2 \). So \( x^2 = 25^2 - 15^2 = 625 - 225 = 400 \), so \( x = \sqrt{400} = 20 \).

Step2: Calculate \( \tan U \)

In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. For angle \( U \), the opposite side is \( WV = 15 \) and the adjacent side is \( VU = 20 \). So \( \tan U=\frac{\text{opposite}}{\text{adjacent}}=\frac{WV}{VU}=\frac{15}{20} = 0.75 \).

Answer:

\( 0.75 \)