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HELPPPP please help me answer this question--example-1

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Answer:


\displaystyle GH = 2 √(30)


\displaystyle FH = 2 √(10)


\displaystyle m \angle G = {30}^( \circ)

Explanation:

QUESTION-2:

we are given a right angle triangle

it's a 30-60-90 triangle of which FH is the shortest side

remember that,in case of 30-60-90 triangle the the longest side is twice as much as the shortest side thus

our equation is


\displaystyle 2FH=4√(10)

divide both sides by 2


\displaystyle(2FH)/(2)= ( 4 √(10) )/(2)


\displaystyle FH =2 √(10)

Question-1:

in order to figure out GH we can use Trigonometry because the given triangle is a right angle triangle

as we want to figure out GH we'll use sin function

remember that,


\displaystyle \sin( \theta) = (opp)/(hypo)

let our opp, hypo and
\theta be GH, 4√10 and 60° respectively

thus substitute:


\displaystyle \sin( {60}^( \circ) ) = (GH)/(4 √(10) )

recall unit circle:


\displaystyle ( √(3) )/(2) = (GH)/(4 √(10) )

cross multiplication:


\displaystyle 2 GH = 4 √(10) * √(3)

simplify multiplication:


\displaystyle 2 GH = 4 √(30)

divide both sides by 2:


\displaystyle GH = 2 √(30)

QUESTION-3:

Recall that, the sum of the interior angles of a triangle is 180°

therefore,


\displaystyle m \angle G + {60}^( \circ) + {90}^( \circ) = {180}^( \circ)

simplify addition:


\displaystyle m \angle G + {150}^( \circ) = {180}^( \circ)

cancel 150° from both sides


\displaystyle m \angle G = {30}^( \circ)

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