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Alecsey [184]
2 years ago
11

Given: △AKL, m∠K=90° AK = KL = 2 M∈ AL , AM = ML Find: ML and KM

Mathematics
2 answers:
djverab [1.8K]2 years ago
8 0

All the trianges involved are isosceles right triangles. You know that the hypotenuse is the leg multplied by √2.

ML = KM = KL/√2 = 2/√2

ML = KM = √2

Kisachek [45]2 years ago
4 0

Remark

AKL is an isosceles right triangle. That's because AK = KL = 2 and K is a right angle.

That makes <A = <L = 45o

Since AM = ML (Given) and KM is common to both Triangle AKM and Triangle LKM, the two triangles are congruent by SSS

Since <AKM = <LKM = 90/2 = 45 (Corresponding parts of congruent triangles are congruent) KM is a perpendicular bisector of AL.

So KM = ML because <MKL and <KLM are both = 45 degrees.

If you find one of KM or ML, you have the other.

KM^2 + LM^2 = 2^2       Remember that KM is perpendicular to AL

2KM^2 = 4

KM^2 = 2

sqrt(KM^2) = sqrt(2)

KM = sqrt(2)

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Since we can construct two right angle triangles between the blimp and the two stadiums as shown in the attached image, then the distance "x" between the two can be find as the difference between the right triangle legs that extend on the ground.

In order to find the size of such legs, one can use the tangent function of the given depression angles as shown below:

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