Question

A geologist at point A measures the distance and angle of elevation to two columns of the Glen Rose formation in Texas. If the distance of side AS is 805 ft and the distance of side AN is 846 ft, compute the difference in the heights of the two columns to the nearest foot. Explain how you found your answer.

Answer 1

Difference in the heights of the columns = 59 ft

Explanation:

Measure of side AS = 805 ft

Measure of side AN = 846 ft

From ΔABS,

sin(51°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

sin(51°) =
`(SB)/(AS)`

sin(51°) =
`(SB)/(805)`

SB = 805×sin(51°)

SB = 625.60 ft

Similarly, from ΔACN,

sin(54°) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

=
`(CN)/(AN)`

CN = ANsin(54°)

CN = 846×sin(54°)

CN = 684.43 ft

Difference in the heights of the columns = CN - SB

= 684.43 - 625.60

= 58.83 ft

≈ 59 ft