Question

in the given figure find the value of sin alpha and cos theta
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Answer 1

Answer:

$\huge\boxed{\sin\alpha=\cos\theta=\dfrac{3}{5}}$

Step-by-step explanation:

In any right triangle with acute angles α and θ

$\sin\alpha=\cos\theta\\\sin\theta=\cos\alpha$

$sine=\dfrac{opposite}{hypotenuse}\\\\cosine=\dfrac{adjacent}{hypotenuse}$

We have

$\text{for}\ \alpha\\adjacent=4cm\\hypotenuse=5cm$

Calculate the opposite using Pythagorean theorem:

$leg^2+leg^2=hypotenuse^2$

substitute:

$4^2+BC^2=5^2\\16+BC^2=25\\BC^2=25-16\\BC^2=9\to BC=\sqrt9\to BC=3\\\\opposite=3cm$

$\sin\alpha=\cos\theta=\dfrac{3}{5}$

Answer 2

Using the properties of trigonometric ratios and angles we calculate the value of $\text{sin }\alpha + \text{cos }\theta$  in ΔABC is 1.2 .

Given:

A right angled triangle with perpendicular of 4 cm length and hypotenuse of length 5cm

To find :

The value of

Solution:

Since the triangle is right-angled at B we can use the Pythagoras's Theorem to calculate the length of the base BC.

We know that :

$AB^2+BC^2=AC^2\\\\or, 4^2+BC^2=5^2\\\\or, BC = \sqrt{9}\\\\or, BC = 3$

Now we will use the properties of trigonometric ratios:

Sin is the ratio of perpendicular to the hypotenuse while cos is the ratio of base to hypotenuse.

$\text{sin }\alpha = BC\div AC\\\\or, \text{sin }\alpha = \frac{3}{5}$

Again ,

$\text{cos }\theta = AB\div AC\\\\or, \text{cos }\theta = \frac{3}{5}$

Therefore:

$\text{sin }\alpha + \text{cos }\theta \\\\= \frac{3}{5} + \frac{3}{5}\\\\=\frac{6}{5} \\\\=1.2$

The value of the expression  $\text{sin }\alpha + \text{cos }\theta$ with respect to ΔABC is 1.2 .

To learn more about trigonometric ratios visit:

brainly.in/question/17628738

brainly.in/question/4563927

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