Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°. John, who is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°. If Jack’s and John’s eyes are 1.5 meters from the ground, how far is John from the base of the tower? Round your answer to the nearest tenth. a.24.5 meters b. 16.1 meters c. 22.2 meters d. 18.8 meters

Respuesta :

my answer would be 20.10 which would equal as 21

The distance between John from the base of the tower will be 18.8 meters. Then the correct option is D.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Jack looks at a clock tower from a distance and determines that the angle of elevation of the top of the tower is 40°.

John, who is standing 20 meters from Jack as shown in the diagram, determines that the angle of elevation to the top of the tower is 60°.

If, Jack’s and John’s eyes are 1.5 meters from the ground.

If Jack's and John's eyes are  meters from the ground and the distance from Jack's eyes to the top of the tower is 50.64 meters,

Then the value of x will be

tan 40° = (x) / (y + 20)      …1

tan 60° = x / y                  …2

From equation 1 and 2, we have

(y + 20)tan 40° = y tan 60°

             y + 20 = 2.06y

       (2.06 – 1)y = 20

                1.06y = 20

                       y = 18.87 meters

The distance between John from the base of the tower will be 18.8 meters.

Then the correct option is D.

The diagram is attached below.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

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