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Answer:
In right angled triangle ABC
tan 26=perpendicular/base
tan26 =BC/1050
BC=1050×tan26=512.12m
again
In right angled triangle ADE
tan 38=perpendicular/base
tan38×700=DE
DE=546.9=547m
now
difference in height =547-512.12m=34.8m=35m
35 m is your answer
Josh sees two hot air balloons in the sky as shown. 35m higher is the balloon on the right than the balloon on the left.
Trigonometric ratios for a right-angled triangle are from the perspective of a particular non-right angle.
In a right-angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slanted side is called the hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called the base.
Josh sees two hot air balloons in the sky as shown.
He determines that the lower hot air balloon is 700 meters away, at an angle of 38 from the vertical.
The higher hot air balloon is 1050 meters away, at an angle of 26 from the vertical.
In right-angled triangle ABC
tan Ф = perpendicular/base
tan26 = BC/1050
BC = 1050 × tan26
BC = 512.12m
In right-angled triangle ADE
tan Ф = perpendicular/base
tan 38 = perpendicular/base
tan38 × 700 = DE
DE = 546.9
DE = 547m
The difference in height = 547 - 512.12m
=34.8m
= 35m
Therefore, 35m higher is the balloon on the right than the balloon on the left.
Learn more about trigonometric ratios here:
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