Answer:
See below
Step-by-step 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
[tex] \displaystyle \: \tan( {30}^{ \circ} ) = \frac{h + 1}{6} [/tex]
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:
[tex] \displaystyle \: \frac{ \sqrt[]{3} }{3} = \frac{h + 1}{6} [/tex]
cross multiplication:
[tex]3(h + 1) = 6 \sqrt{3} [/tex]
divide both sides by 3:
[tex]h + 1 = 2 \sqrt{3} [/tex]
cancel 1 from both sides:
[tex] \therefore \: h = 2 \sqrt{3} - 1[/tex]
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
