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aivan3 [116]
3 years ago
11

HELPPPP please help me answer this question-

Mathematics
2 answers:
erik [133]3 years ago
6 0

Answer:

\displaystyle   GH  =  2 \sqrt{30}

\displaystyle FH = 2 \sqrt{10}

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

Step-by-step explanation:

<h3>QUESTION-2:</h3>

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\sqrt{10}

divide both sides by 2

\displaystyle\frac{2FH}{2}= \frac{ 4 \sqrt{10} }{2}

\displaystyle FH =2 \sqrt{10}

<h3>Question-1:</h3>

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)  =  \frac{opp}{hypo}

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

thus substitute:

\displaystyle  \sin(  {60}^{ \circ} )  =  \frac{GH}{4 \sqrt{10} }

recall unit circle:

\displaystyle   \frac{ \sqrt{3} }{2}   =  \frac{GH}{4 \sqrt{10} }

cross multiplication:

\displaystyle   2 GH  =  4 \sqrt{10}  \times  \sqrt{3}

simplify multiplication:

\displaystyle   2 GH  =  4 \sqrt{30}

divide both sides by 2:

\displaystyle   GH  =  2 \sqrt{30}

<h3>QUESTION-3:</h3>

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}

noname [10]3 years ago
6 0

ANSWER:

It is a 30-60-90 right angle triangle with base FH.

So, 2FH = 4√10

FH = 2√10.

Now, sin60° = GH/4√10

√3/2 = GH/4√10

GH = √3/2 × 4√10

GH = 2√30.

By angle sum property,

m∠G = 180° - 150°

m∠G = 30°.

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