Question

This is the only thing i do not understand about geometry

Answer 1

see explanation

Explanation:

Using the tangent ratio in the right triangle

tan40° =
`(opposite)/(adjacent)` =
`(opp)/(20)` ( multiply both sides by 20 )

20 × tan40° = opp , thus

opp = 20 × 0.839 ≈ 16.78 , then

height of traffic light = 16,78 + 5 = 21.78 ft

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Using the tangent ratio in the right triangle

tan42.71° =
`(opposite)/(adjacent)` =
`(150)/(d)` ( d is the distance between store and bank )

Multiply both sides by d

d × tan42.71° = 150 ( divide both sides by tan42.71° )

d =
`(150)/(tan42.71)` =
`(150)/(0.923)` = 162.5 m