Question

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle. The length of K M is 6 and the length of M J is 3. What is the length of line segment LJ? 9 units 12 units 15 units 18 units

Answer 1

Answer:

$LJ=15\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the length side KJ

In the right triangle JKM

Applying the Pythagoras Theorem

$KJ^{2}=JM^{2}+KM^{2}$

we have

$JM=3\ units$

$KM=6\ units$

substitute

$KJ^{2}=3^{2}+6^{2}$

$KJ^{2}=45}$

$KJ=\sqrt{45}\ units$

simplify

$KJ=3\sqrt{5}\ units$

step 2

Find the value of cosine of angle MJK in the right triangle JKM

$cos(JKM)=JM/KJ$

substitute the values

$cos(JKM)=\frac{3}{3\sqrt{5}}$

simplify

$cos(JKM)=\frac{\sqrt{5}}{5}$ -----> equation A

step 3

Find the value of cosine of angle MJK in the right triangle JKL

$cos(JKM)=KJ/LJ$

we have

$KJ=3\sqrt{5}\ units$

$cos(JKM)=\frac{\sqrt{5}}{5}$ ----> remember equation A

substitute the values

$\frac{\sqrt{5}}{5}=\frac{3\sqrt{5}}{LJ}$

Simplify

$LJ=5(3)=15\ units$

Answer 2

Answer:

c.

Step-by-step explanation: