Question

if tan theta 8 upon 15 find sin theta & cos theta

Answer 1

tan theta =8/15
p/b=AB/BC=8/15
AB =8, BC=15
AC^2 =AB^2 +BC^2
AC^2 = 8^2 +15^2
AC^2 =64+225
AC = root 289
Ac=17

sin theta =AB/AC
= 8/17

cos theta =BC/AC
= 15/17

Answer 2

Answer:

The values are:

$Sin(\theta) = \frac{8}{17}$

and

$cos(\theta) = \frac{15}{17}$

Explanation:

It is given that:

$Tan(\theta) = \frac{8}{15}$

Now, we can use the right-angled triangle to find the trigonometric ratios.

So, In a right-angled triangle ABC;

$Tan(\theta)$ is the ratio of Perpendicular to Base.

So, In Triangle ABC;

AB = Perpendicular;

BC = Base;

AC = Hypotenuse;

So,

$\frac{AB}{BC} = \frac{8}{15}$

which means;

AB = 8k;

BC = 15k;

Using the Pythagoras theorem,

AC² = AB² + BC²

AC² = 8² + 15²

AC² = 64 + 225;

AC² = 289;

AC = 17;

and,

Sin is the ratio of perpendicular and hypotenuse;

Cos is the ratio of Base and Hypotenuse;

So,

$Sin(\theta) = \frac{8}{17}$

$cos(\theta) = \frac{15}{17}$

Therefore,

The values are:

$Sin(\theta) = \frac{8}{17}$

and

$cos(\theta) = \frac{15}{17}$

To learn more about Trigonometry, visit:

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