Question

Given scalene right triangle with an acute angle of 65°.

To the nearest tenth of a foot, determine the value of h.

Answer 1

Tan (65) = h/4

h = Tan(65) * 4

h = 2.1445 * 4

h = 8.578

h = 8.6 (rounded to the nearest tenth)

Answer:

8.6 ft

Answer 2

Answer: 8.6 feet

Explanation:

By trigonometry , we know that in a right triangle the tangent of an angle x is equal to the ratio of the side opposite to the side adjacent to angle x .

In the given right triangle ,Angle :
`=65^(\circ)`

The side adjacent to
`65^(\circ)= 4\text{ ft}`

Then , we have

`\tan65^(\circ)=(h)/(4)\\\\\Rightarrow\ 2.14450692051=(h)/(4)\\\\\Rightarrow\ h=4*2.14450692051\\\\\Rightarrow\ h=8.57802768204\approx8.6\text{ feet}`

Hence, the value of h = 8.6 feet.