I need help with the following problem: From a point 50 meters from the bottom of a radio tower along level ground, the angle of elevation to the top of the tower is 67 degrees. What is the height of the tower?
think back, back, back to your days in trig.
If the tower has height h,
tan 67 = h/50
h = 117.8 m
to solve this problem we need trigonometry therefore takes the radiant
67°*3,14/180=1,17 rad.= a
point P=50m
height tower H=?
L=hypotenuse of the right triangle LPH
P=Lcos(a)=> (i)L=p/cos(a)
(ii)H=Lsen(a)
(i)+(ii)H=[p/cs(a)]*sn(a)
tan(a)=sn(a)/cs(a)===>H=p*tan(a)=118m
From my view. Tan=opp/adj
Therefore when u cross multiply u have
50tan67
H=82.6m
Approx. 83m
To solve this problem, we can use trigonometry and the concept of right triangles. Let's call the height of the tower "h".
We have a right triangle formed by the ground, the tower, and the line of sight from the point to the top of the tower. The angle of elevation is the angle between the ground and the line of sight.
From the problem, we know that the distance from the point to the bottom of the tower (the base of the triangle) is 50 meters and the angle of elevation is 67 degrees.
Using trigonometry, we can use the tangent function to relate the angle of elevation to the opposite and adjacent sides of the triangle. In this case, the opposite side is the height of the tower (h) and the adjacent side is the distance from the point to the bottom of the tower (50 meters).
The tangent of the angle of elevation is defined as the ratio of the opposite side to the adjacent side:
tan(angle of elevation) = h / 50
Rearranging the equation to solve for h, we have:
h = 50 * tan(angle of elevation)
Plugging in the given values, we get:
h = 50 * tan(67 degrees)
Now, we can use a calculator to find the tangent of 67 degrees and multiply it by 50 to get the height of the tower.
Using the calculator, we find that the tangent of 67 degrees is approximately 2.14. Multiplying 2.14 by 50, we get:
h ≈ 107 meters
Therefore, the height of the tower is approximately 107 meters.