Question

(h + 1) cm 6 cm A Write and solve an equation to find the value of h Include all of your work in your answer. B. In two or more complete sentences, verify your answer using mental math. 2​

Answer 1

See below

Explanation:

we are given opposite and adjacent if the given right angle triangle

we want to make an equation with the given information

Part-1:

notice that adjacent is greater than opposite so we can only take 30° as our angle

hence,

using trigonometric property

our equation is

`\displaystyle \: \tan( {30}^( \circ) ) = (h + 1)/(6)`

we took tangent function because we know that tangent function is the ratio of opposite and adjacent

now let's solve the equation

recall unit circle:

`\displaystyle \: \frac{ \sqrt[]{3} }{3} = (h + 1)/(6)`

cross multiplication:

`3(h + 1) = 6 √(3)`

divide both sides by 3:

`h + 1 = 2 √(3)`

cancel 1 from both sides:

`\therefore \: h = 2 √(3) - 1`

Part-2:

by using mental math

The angle of elevation at the top of a tower at a point on the ground is 30° at a distance of 6 metre from the foot and the height of the tower is h+1. find h

now this question verifies the equation

because we are given a right angle triangle where the opposite is less than the adjacent so we took 30° as our angle

by solving the equation we'll again get our answer