Question

Given triangle ABC A. State the values of sinC, cosC, and tanC. B. Find angle C, rounded to the nearest degree. C. Find angle A.

Answer 1

Given:

The sides of the right triangle is given as 8,15,17.

The objective is,

a) To find the values of sinC, cosC, tanC.

b) To find angle C.

c) To find angle A.

Step-by-step explanation:

a)

With respect to angle C, AB is the opposite side and AC is the hypotenuse side.

To find sinC:

The trigonometric value of sinC can be calculated as,

`\begin{gathered} \sin C=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin C=(AB)/(AC)\text{ . . }\ldots(1) \end{gathered}`

On plugging the given values in equation (1),

`\sin C=(8)/(17)`

To find cosC:

The trigonometric value of cosC can be calculated as,

`\begin{gathered} \cos C=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \cos C=(BC)/(AC)\text{ . . . . . .(2)} \end{gathered}`

On plugging the given values in equation (2),

`\cos C=(15)/(17)`

To find tanC:

The trigonometric value of tanC can be calculated as,

`\begin{gathered} \tan C=\frac{\text{opposite}}{\text{adjacent}} \\ \tan C=(AB)/(BC)\text{ .. . . }\ldots\text{ (3)} \end{gathered}`

On plugging the given values in equation (3),

`\tan C=(8)/(15)`

b)

To find the value of angle C

On solving any of the obtained trigonometric values obtained.

Consider the trigonometric ratio of tan.

`\begin{gathered} \tan C=(8)/(15) \\ C=\tan ^(-1)((8)/(15)) \end{gathered}`

On further solving the above expression,

`\begin{gathered} C=28.072486\ldots\text{..} \\ C\approx28\degree \end{gathered}`

c)

To find the value of angle A:

By the angle sum property of a triangle, the sum of the angles of a triangle will be 180°.

`\begin{gathered} A+B+C=180\degree \\ A=180\degree-B-C\text{ . . . . (4)} \end{gathered}`

On plugging the obtained values in equation (4),

`\begin{gathered} A=180\degree-90\degree-28\degree \\ =62\degree \end{gathered}`

Hence,

a) The value of sinC = 8/17, cosC = 15/17, tanC = 8/15.

b) The value of angle C is 28°.

c) The value of angle A is 62°.