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A tree is growing such that its trunk forms a 98 degree angle with the ground. At a point 27 meters from the tree, the angle of elevation to the top of the tree is 24 degrees. If a bug crawls from the base of the tree all the way to the top, how far has it gone? (i.e. how tall is the tree?)A. 46 metersB. 13 metersC. 54 metersD. 56 meters

Respuesta :

Answer: option B is the correct answer

Step-by-step explanation:

The diagram of the tree is shown in the attached photo. The triangle ABC formed is not a right angle triangle. The last angle, angle C is gotten by subtracting the sum of angle A and angle B from 180(sum of angles) in a triangle is 180). It becomes

C = 180-(98+24)= 180 -122

C = 58 degrees

To find the height of the tree, we would apply the sine rule

a/sinA = b/sin B = c/ sinC

We would apply b/sin B = c/ sinC

b/sin24 = 27/sin58

b/0.4067 = 27/0.8480

Cross-multiplying,

27 ×0.4067 = b × 0.8480

10.9809 = 0.8480b

b = 10.9809/0.8480 = 12.949

Approximately 13 meters

The bug crawls 13 meters from the base to the top of the tree

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