Question

Problem: you must find the horizontal distance between two towers (points a and b) at the same elevation on opposite sides of a wide canyon running east and west. The towers lie directly north and south of each other. You mark off an east/west line CD running perpendicular to AB.
A) From C you measure the angle between the two towers (angle ACB) as 88.60 degrees. Given the distance from C to B is 389 feet, write an equation and solve it to find an expression for the distance AB to the nearest whole foot. (Note: AB is perpendicular to CD)

B) You want to check your work to make sure it’s right. You should be able to both measure and compute the angle at D. Knowing the distance between the two towers from above and the distance BD is 459 feet, what is the angle at D to the nearest hundredth degree?

C) What is angle CAD in radians? Give your answer rounded correctly to 4 decimal places.

Answer 1

The expression for distance AB is :389 tan 88.60°. The angle D is 88.35°.The value of angle CAD in radians is 0.0532 rad.

Step-by-step explanation:

Given the information, you can sketch triangle ACB with ∠C=88.60° and a perpendicular bisector of segment CD as AB that forms 90° at B where the diatnace from C to B given as 389 ft you can find the length of the perpendicular bisector AB which is the distance between tower A and B.

Apply the tangent of an angle rule, where tangent of angle = opposite side length/adjacent side length

tan 88.60°=O/A

tan 88.60°=AB/389

AB=389 tan 88.60° = 15916.87 ⇒ 15917 (nearest foot)

B.

Given distance BD as 459 ft and the distance between tower A and B as 15917 ft you can calculate the value of angle ∠D by applying the tangent of an angle formula.

tan Ф=O/A where Ф=∠D

tan ∠D =15917/459

tan ∠D =34.6772834701

tan⁻(34.6772834701) =88.35°

C.

Finding angle ∠A in radians will be;

Applying the sum of angles in a triangle theorem

∠A=180°-(88.60°+88.35°) = 180°-176.95°=3.05°

Changing degrees to radians, multiply value of degrees by π/180°

3.05×π/180 =0.05323254 ⇒ 0.0532 rad

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Tangent of an angle formula :brainly.com/question/12003325

Keywords : horizontal distance,towers, elevation, perpendicular line, distance, equation, expression,hundredth

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