Question

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

Answer 1

Answer:

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 2

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.

For more information, refer to the link given below:

https://brainly.com/question/13710437