a flagpole at a right angle to the hrizontal is located on a slope that makes an angle of 14 degree with the horizontal the flagpole casts a 16m shadow up the slope wen the angle of elevation from the tip of the shawdow to the sun is 20 degree find the height of the flagpole
Your question is almost impossible to read without capitalization and punctuation. It also has three misspelled words.
Do you do math in the same careless manner?
Draw a diagram.
T = top of pole
B = bottom of pole
S = tip of shadow
Draw a horizontal line from S to intersect the pole at P.
The height of the pole is BP+PT
BP = 16 sin14°
PS = 16 cos14°
PT = PS tan20°
Im sorry for that Ms.Sue
16/sin70degree= x/sin34degree
is equal to 9.5 meters that is the answer
To find the height of the flagpole, we can use trigonometry and the given information.
Let's break down the problem step by step:
1. Draw a diagram: Draw a right triangle with the flagpole as the vertical side, the shadow as the horizontal side, and the slope as the hypotenuse.
|
/|\
/ | \
height / | \ shadow
/ | \
/ | \
/ | \
/θ | \
/_ _ _ _|_ _ _ _\
slope
2. Identify the given information:
- The angle of the slope with the horizontal = 14 degrees (angle θ).
- The length of the shadow cast by the flagpole = 16m.
- The angle of elevation from the tip of the shadow to the sun = 20 degrees.
3. Determine the angle between the shadow and the slope:
The angle between the shadow and the slope is the sum of angles θ (slope) and the angle of elevation.
Angle between shadow and slope = 14 degrees + 20 degrees = 34 degrees.
4. Determine the length of the flagpole (height):
Since we have the length of the shadow and the angle between the shadow and slope, we can use trigonometry to find the length of the flagpole (height).
In a right triangle, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side:
tan(34 degrees) = height / shadow
tan(34 degrees) = height / 16m
To solve for height:
height = tan(34 degrees) * 16m
Calculating with a scientific calculator:
height ≈ 10.4m.
Therefore, the height of the flagpole is approximately 10.4 meters.