The largest egyptian pyramid is 146.5 m high. when nika stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20 degrees with the ground. what is the horizontal distance between the center of the pyramid and nika? round to the nearest meter.
*you would have to use sohcahtoa to figure this out
Since we know that we need to find the adjacent side of the triangle and also since we already know the opposite side of the triangle from the angle, we can use tan.
403 meters away form the pyramid
The correct answer is 402.5 but the answer is 402.
In order to solve this, you have to use the law of sines, the shadow cast would be the opp side to the 20º angle that you the have over the tree and the height of the tree so we would use tan to solve this:
So we clear Height from the equation:
So now we know that the height of the tree would be 72,8 feet.
The value of height of the building h = 509.2 feet
From the Δ A B C
⇒ h = y ° ------- (1)
From Δ A B D
⇒ h = ( y + 300 ) ° ------- (2)
Equation 1 = Equation 2
⇒ y ° = ( y + 300 ) °
⇒ 0.46 y = 0.36 y + 109.2
⇒ 0.1 y = 109.2
⇒ y = 1092 feet
Put this value of y in equation ( 1 ) we get,
⇒ h = 1092 × tan 25°
⇒ h = 509.2 feet
This is the value of height of the building.
≈ 345.8 ft
There is a right triangle formed by Bonnie's height (h) the ground and the angle of elevation.
Using the tangent ratio in the right triangle
tan20° = = ( multiply both sides by 950 )
950 × tan20° = h , thus
h ≈ 345.8 ft ( to 1 dec. place )
tan(20°) = (tree height)/(200 ft)
(tree height) = (200 ft)*tan(20°) ≈ 72.8 ft
I'm not sure how many digits after the decimal you need, so I typed out five.
sin(20) = opposite/hypotenuse
sin(20) = x/2.6
0.342 = x/2.6
0.8892 = x
0.8892 meters is the correct answer.
ask goog great chance of finding the solution there