Questions: What is the value of z?

Transcript text: What is the value of $z$ ?

Solution

Solution Steps

Step 1: Identify similar triangles

Triangle WUT and triangle WVT share angle W. Angle WTU and angle WTV are both right angles, so they are congruent. Therefore, triangle WUT is similar to triangle WVT by Angle-Angle similarity.

Step 2: Set up a proportion

Since triangle WUT and triangle WVT are similar, the ratio of corresponding sides must be equal. This leads to the proportion: WT/WU = WV/WT

Step 3: Substitute known values

We are given WT = 5, WU = 5, and WV = 8z. Substituting these values into the proportion from Step 2, we have: 5/5 = 8z/5

Step 4: Simplify and solve for z

The proportion simplifies to 1 = 8z/5. Multiplying both sides by 5 gives 5 = 8z. Dividing both sides by 8 yields z = 5/8

Final Answer: The value of z is 5/8.

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