In ΔRST, the measure of ∠T=90°, TS = 65, SR = 97, and RT = 72. What ratio represents the cotangent of ∠S?

Mathematics

1 answer:

horrorfan [7]3 years ago

5 0

Answer:

65/72

Step-by-step explanation:

Given that ∠T=90° then the triangle ΔRST is a right angled triangle. Considering ∠S, RT is the opposite side, TS is the adjacent side and RS is the hypotenuse side. Using the notation

SOH CAH TOA

Tan ∠S = 72/65

Hence the cotangent of ∠S which is the inverse of the tangent will be

= 65/72

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For this case we have to define root properties:

$\sqrt [n] {a ^ n} = a ^ {\frac {n} {n}} = a$

In addition, we know that:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

On the other hand:

$4 ^ 2 = 16$

Thus, we can rewrite the given expression as:

$\sqrt {4 ^ 2 * a ^ 8 * \frac {1} {b ^ 2}} =\\4 ^ {\frac {2} {2}} * a ^ {\frac {8} {2}} * \frac {1} {b ^ {\frac {2} {2}}} =\\4 * a ^ 4 * \frac {1} {b}$