Question

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

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

Step-by-step 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

$\tan65^{\circ}=\dfrac{h}{4}\\\\\Rightarrow\ 2.14450692051=\dfrac{h}{4}\\\\\Rightarrow\ h=4\times2.14450692051\\\\\Rightarrow\ h=8.57802768204\approx8.6\text{ feet}$

Hence, the value of h = 8.6 feet.