Let m∠CLN = x. Then m∠ALM = 3x, and m∠A = 90°-x, m∠C = 90°-3x.
The sum of angles of ∆ABC is 180°, so we have
... 180° = 40° + m∠A + m∠C
Using the above expressions for m∠A and m∠C, we can write ...
... 180° = 40° + (90° -x) + (90° -3x)
... 4x = 40° . . . . . . . . . add 4x-180°
... x = 10°
From which we conclude ...
... m∠C = 90°-3x = 90° - 3·10° = 60°
The ratio of CN to CL is
... CN/CL = cos(∠C) = cos(60°)
... CN/CL = 1/2
so ...
... CN = (1/2)CL
Answer:
Step-by-step explanation:
Let's translate what you've written in words to an expression with mathematical symbols.
To solve this, you need to multiply both the numerator and denominator with the conjugate of the denominator.
<u>Given</u>:
It is given that KLM is a right triangle.
The measure of ∠M is 90°
The length of LK is 89, ML is 80 and KM is 39.
We need to determine the ratio that represents the tangent of ∠K.
<u>Measure of tan ∠K:</u>
The measure of tan ∠K can be determined using the trigonometric ratio.
Thus, we have;
From the figure attached below, the side opposite to ∠K is ML and the side adjacent to ∠K is KM
Hence, substituting the values, we get;
where ML = 80 and KM = 39.
Substituting, we get;
Thus, the ratio that represents the tangent of ∠K is
