You are standing 45 meters from the base of the empire state building. you estimate that the angle of elevation to the top of the 86th floor(the observatory) is 82°. if the total height of the building is another 123 meters above the 86th floor, what is the total height of the building?
a) [45tan(82°) + 123] meters
b) [123tan(82°) + 45] meters
c) [45cos(82°) + 123] meters
d) [123cos(82°) + 45] meters

[45tan(82°)+123] meters

A is correct

Step-by-step explanation:

You are standing 45 meters from the base of the Empire State Building.

You estimate that the angle of elevation to the top of the 86th floor(the observatory) is 82°.

If the total height of the building is another 123 meters above the 86th floor.

OB = 45 m , ∠O= 82°

In Δ OBA, ∠B = 90°

Top of the building, T at 123 m from A

Total height of building = BA + AT

Hence, The height of building from ground is [45tan82°+123] meters

could

step-by-step explanation:

u send me a picture of ur work

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°