A woman wants to measure the height of a nearby tower. She places a 5 ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. The total length of the tower's shadow is 177 ft , and the pole casts a shadow that is 6.5 ft long. How tall is the tower? Round your answer to the nearest foot.

this scenario sets up a pair of similar right triangles. the smaller triangle had height 5 and base 6,5. the larger had height x (height of the tower, which we want to measure). and base of 177 the proportion is then x/177 = 5/6.5, or
6.5x = 5*177
6.5x=885
x=136.15
answer is 136 feet

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Anshuyadav Anshuyadav · Answer 2 · 2022-05-31T17:49:08+02:00

The tower is 136ft tall.

What are the similar triangles?

Similar triangles are the triangles that have the same shape, but different sizes. The corresponding angles are congruent and the sides are in proportion.

What is the ratio of any two corresponding sides of similar triangles?

The ratio of any corresponding sides in two equiangular triangles is always the same.

Let's visualize the situation according to the given question.

AB is the pole, whose length is 5f

BC is the shadow of the pole AB, whose length is 6.5ft

QR is the shadow of the tower PQ, whose length is 177ft

Let the height of the tower PR be h feet.

In triangle ACB and triangle PRQ

∠ACB = ∠PRQ = 90 degrees

( the objects and shadows are perpendicular to each other)

∠BAC = ∠QPR

( sunray falls on the pole and tower at the same angle, at the same time )

⇒ΔACB similar to ΔPRQ ( AA criterion)

Therefore, the ratio of any two corresponding sides in equiangular triangles is always same.

⇒ AC/CB = PR/RQ

⇒[tex]\frac{5}{6.5} = \frac{h}{177}[/tex]

⇒ [tex]h = \frac{(5)(177)}{6.5}[/tex]

⇒ h = 136.15 ft

Hence, the tower is 136ft tall.

Learn more about similar triangles here:

https://brainly.com/question/25882965

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