Mathematics, 29.05.2020 04:58 cbaillie8462

What is the length of Line segment G J? 2 units 4 units 6 units 8 units

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Answer from: nschavez123

The length of the segment GJ is 8 units and this can be determined by using the trigonometric function.

Given :

Right isosceles triangle FGH.The length of the segment FH is 16 units.

The following steps can be used in order to determine the length of the line segment GJ:

Step 1 - Apply the sum of the interior angle properties on the triangle FGH.

$\begin{aligned}\\\angle G + \angle F + \angle H &= 180\\90 + 2\angle F &= 180\\\angle F &= 45^\circ\\\end{aligned}$

Step 2 - The trigonometric functions can be used in order to determine the length of the line segment GJ.

$\tan\theta = \dfrac{GJ}{JH}$

Step 3 - Now, substitute the value of JH and $\theta$ in the above expression.

$\tan45= \dfrac{GJ}{8}$

Step 4 - Simplify the above expression.

$\dfrac{GJ}{8}=1\\\\GJ \;= 8$

So, the length of the segment GJ is 8 units.

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What is the length of Line segment G J? 2 units 4 units 6 units 8 units

Answer from: simrankaurdhatt

Option D. 8 units

Step-by-step explanation:

The given question is incomplete: here is the complete question.

Triangle FGH is an isosceles right triangle with a hypotenuse that measures 16 units. An altitude, GJ, is drawn from the right angle to the hypotenuse.

What is the length of GJ?

A. 2 units

B. 4 units

C. 6 units

D. 8 units

ΔFGH in the figure attached, is a right isosceles triangle.

m∠G = 90° and hypotenuse FH = 16 units

GI is an altitude drawn from point G to the hypotenuse.

Since this triangle is an isosceles right triangle, measure of ∠F and ∠H will be equal.

m∠F + m∠G + m∠H = 180°

m∠F + 90° + m∠F = 180°

2m∠F = 180°- 90°

2m∠F = 90°

m∠F = 45°

GJ is an altitude which will divide the hypotenuse in two equal parts. (By the property of a right isosceles triangle)

FJ ≅ GJ ≅ 8 units

Now in right triangle GJH,

tan H = $\frac{GJ}{JH}$

tan 45° = $\frac{GJ}{8}$

1 = $\frac{GJ}{8}$

GJ = 8 units

Therefore, length of altitude GJ will be 8 units.

Answer from: Quest

table 1

step-by-step explanation:

1-16

2-32

4-64

8-128

all multiples of 16

There are 16 tablespoons in one cup. which table correctly relates the number of cups to the number

Answer from: Quest

step-by-step explanation:

distance formula is d=√(x2-x1)^2 + (y2-y1)^2

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