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sammy [17]
3 years ago
15

You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the groun

d and use trig to calculate the height. The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees. This forms a right triangle. (a) What is the measure of the other acute angle?(b) What is the height of the tree?

Mathematics
1 answer:
padilas [110]3 years ago
3 0

Answer:

(a)55^o

(b)350.1ft

Step-by-step explanation:

The sum of the angles inside a triangle must be 180°, but from the right angle we already have 90°, so the sum of the two acute angles is 90°, then:

90^o-35^o=55^o

Let s be the length of the shadow and h the height of the three, so tan(35) is

tan(35^o)=\frac{h}{s}

Solving that last equation for h:

h=s*tan(35)=500(0.7002)=350.1ft

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