A 650-ft guy wire is attached to the top of a communications tower. If the wire makes an angle of 70° with the ground, how tall is the communications tower? (Round your answer to the nearest foot.)

The height of the tower would be 610.80 feet.

Step-by-step explanation:

Consider h be the height( in ft )  of the communications tower,

Given,

Length of the wire = 650 ft,

Angle made by the wire to the ground = 70°

Thus, we make a triangle with sides h and 650 with angle 70°  opposite to the side measures h, ( shown below )

Using trigonometric ratio,

Hence, the height of the tower would be 610.80 feet.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).