question

[pippo19]

Sam is flying a kite on a 40-m string. The angle of elevation of hte kite measures 35 degrees, and Sam's hand is 1.8m above the ground. About how high is the kite off the ground? Round your answer to the nearest tenth of a meter.

How do you do problems like these?

 

[soroban]

Hello, pippo19!

Sam is flying a kite on a 40-m string.
The angle of elevation of hte kite measures 35°, and Sam's hand is 1.8m above the ground.
About how high is the kite off the ground? Round your answer to the nearest tenth of a meter.

How do you do problems like these?

First, make a sketch . . .

. . . . . . . . . . . . . . . * K
. . . . . . . . . . . . . * . |
. . . . . . . . . . . * . . . |
. . . . . . .40 * . . . . . | y
. . . . . . . * . . . . . . . |
. . . . . * 35°. . . . . . |
. .H * - - - - - - - - - -* A
. . . | . . . . . . . . . . . |
.1.8| . . . . . . . . . . . |1.8
. . . | . . . . . . . . . . . |
. . . * - - - - - - - - - -*


The kite is at K . . . Sam's hand is at H . . . HK = 40m . . . Angle KHA = 35°.

Let y = KA. .We see that the height of the kite is: y + 1.8m.
. . . . . . . . . . . . . . . . . . . . . . . . . . .y
In right triangle KAH: .sin 35° .= .---
. . . . . . . . . . . . . . . . . . . . . . . . . . 40

Hence: .y .= .40*sin35° .= .22.943

Therefore: .Height .= .22.943 + 1.8 .≈ .24.7m

 

[pippo19]

Thank you for your help.