To measure a stone face carved on the side of a mountain, two sightings 700 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 35degreesand the angle of elevation to the top is 38 degrees, what is the height of the stone face

Height of stone face is : 56.7 ft

Step-by-step explanation:

Kindly refer to the attached image for the diagram of the given conditions and values.

Let C be the base of mountain.

D be the point from where two sightings are taken.

AB be the stone face.

Angle of elevations:

To find:

Height of stone face = ?

AB = ?

Solution:

We can use trigonometric function of tangent here in two triangles :

So, Height of stone face is : 56.7 ft

x = 25/2304

step-by-step explanation:

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°