If a bird is on the ground, 7 ft away from a 10 ft tall tree, then what is the angle (to the
nearest degree) at which the bird is looking up at the top of the tree?

The angle is 55°

Step-by-step explanation:

To find the angle at which a bid is looking up on top of a tree that is 10feet tall if the bird is on the ground 7 feet away from the tree, we will follow the steps below:

we will use trigonometric ratio to find the angle

SOH CAH TOA

sinФ = opposite / hypotenuse

cosФ = adjacent / hypotenuse

tanФ = opposite /adjacent

from the diagram below, opposite = 10 feet   and   adjacent = 7 feet

the best trig.ratio to use is tan

tanФ = opposite /adjacent

tanФ = 10 /7

tan Ф =1.42857

to get the value of  Ф, we will take the tan⁻¹  of both-side

tan⁻¹ tan Ф = tan⁻¹ 1.42857

Ф= tan⁻¹ 1.42857

Ф≈55°

Therefore, the angle is 55°

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

the radius is 2 times the diameter.

step-by-step explanation: