Question

In ΔKLM, the measure of ∠M=90°, LK = 85, KM = 13, and ML = 84. What ratio represents the cosine of ∠K?

Answer 1

cos K = 13/85

Explanation:

KLM is a triangle with the ∠M = 90°. LK = 85, KM = 13 and ML = 84 . The ratio that represent the cosine of ∠K can be calculated below.

The triangle is a right angle triangle. The triangle has an opposite sides, adjacent sides and an hypotenuse.

KM = adjacent side

ML = opposite side

LK = hypotenuse

The ratio of the cosine of ∠ K can be gotten using the SOHCAHTOA principle.

cos K = adjacent/hypotenuse

adjacent = 13

hypotenuse = 85

cos K = 13/85

Answer 2

13/85

Explanation:

We can solve the triangle using the trigonometrical ratios which may be expressed in the form SOA CAH TOA Where,

SOA

Sin Ф = opposite side/hypotenuses side

CAH

Cosine Ф = adjacent side/hypotenuses side

TOA

Tangent Ф = opposite side/adjacent side

The hypotenuse is the side facing the right angle while the opposite is the side facing the given angle.

Hence considering ∠K,

KM is the adjacent side, KL is the hypotenuse side and ML is the opposite side.

cosine of ∠K = KM/KL

= 13/85