Question

Given the triangle and equation below, what is the value of x?

tan∠A - csc∠C = 3x

Answer 1

@lgbasallote

Answer 2

do you have an answer?

Answer 3

no what do i do?

Answer 4

find tan A first

Answer 5

is A the letter on the triangle?

Answer 6

yup

Answer 7

ok A is 5

Answer 8

@waterineyes can you help? im getting confused lol

Answer 9

\[\tan(A) = \frac{7}{5}\]

Now find the hypotenuse:

Using Pythagoras Theorem:

\[H = \sqrt{7^2 + 5^2} = \sqrt{74}\]

So,

\[cosec(C) = \frac{Hypotenuse}{Perpendicular} = \frac{\sqrt{74}}{5}\]

According to the question:

\[\tan(A) - cosec(C) = 3x\]

\[\frac{7}{5} - \frac{\sqrt{74}}{5} = 3x \implies \frac{7 - \sqrt{74}}{5} = 3x\]

\[x = \frac{7 - \sqrt{74}}{15}\]

Answer 10

From the figure:\[\text{Tan}\left[\text{ArcTan}\left[\frac{7}{5}\right]\right]-\text{Csc}\left[\text{ArcCot}\left[\frac{7}{5}\right]\right]=3x \]\[\frac{7}{5}-\frac{\sqrt{74}}{5}=3 x \]\[x=\frac{1}{15} \left(7-\sqrt{74}\right) \]