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A flagpole stands on the edge of vertical cliff. From a point 30 m away from the cliff, the angle of elevation of the top of the flagpole is 35° and that of the top of cliff is 20°. How tall is the flagpole to the nearest metre? Give your answer, in metres.

Sagot :

The flagpole is 35.43 meters tall

Distance of the flag from the cliff is 30m

Angle of elevation to the flagpole is 35°

Angle of elevation to the top of the cliff is 20°

To solve this we would apply the sine rule.

The sine rule states that [tex]\frac{sin A}{a} = \frac{sin B}{B}[/tex]

Taking a look at the attached image, we see that

b = 30

B = 70°

a = ?

A = 20°

Applying the formula, we have

[tex]\frac{sin20}{a} = \frac{sin 70}{30}[/tex]

asin(70) = 30sin(20)

a = [tex]\frac{30sin20}{sin70}[/tex]

a = [tex]\frac{27.388}{0.773}[/tex]

a = 35.43 meters

View image Barackodam
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