Question

find the value of tan v rounded to the nearest hundredth, if necessary. triangle with right angle at u, ut=28, vt=35

Explanation:

Step1: Find the length of VU

In right triangle \( VUT \), we know the hypotenuse \( VT = 35 \) and the leg \( UT = 28 \). We can use the Pythagorean theorem \( a^{2}+b^{2}=c^{2} \), where \( c \) is the hypotenuse and \( a,b \) are the legs. Let \( VU = x \), then \( x^{2}+28^{2}=35^{2} \). So \( x^{2}=35^{2}-28^{2}=(35 - 28)(35 + 28)=7\times63 = 441 \), then \( x=\sqrt{441}=21 \).

Step2: Calculate \( \tan V \)

The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. For angle \( V \), the opposite side is \( UT = 28 \) and the adjacent side is \( VU = 21 \). So \( \tan V=\frac{\text{opposite}}{\text{adjacent}}=\frac{UT}{VU}=\frac{28}{21}=\frac{4}{3}\approx1.33 \) (rounded to the nearest hundredth).

Answer:

\( 1.33 \)