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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

User Samps
by
8.6k points

2 Answers

0 votes

Answer:

The answer would be option C. 15 units :)

Explanation:

Did it on edge :D

Hope this helps!

User Jaykishan
by
8.0k points
3 votes

Answer:


LJ=15\ units

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=√(45)\ units

simplify


KJ=3√(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)=(3)/(3√(5))

simplify


cos(JKM)=(√(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√(5)\ units


cos(JKM)=(√(5))/(5) ----> remember equation A

substitute the values


(√(5))/(5)=(3√(5))/(LJ)

Simplify


LJ=5(3)=15\ units

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point-example-1
User Tanuki
by
7.9k points

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