Question

In the given figure, find the value of sin∝ + cosθ ?​

Answer 1

Answer:

AB= 4 cm

BC = √(5^2 -4^2) =√(25 - 16)= √9 = 3 cm

AC = 5 cm

sin∝ = 3/5

cosθ = 3/5

sin∝ +cosθ = 3/5 + 3/5 = 6/5

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 $\text{sin }\alpha + \text{cos } \theta$

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 :

$AB^2+BC^2=AC^2$

$or, 4^2+BC^2=5^2\\\\or,BC^2 = 25-16\\\\or, BC = 9 \text { cm}$

Now from trigonometric ratios we know that :

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

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

Again ,

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

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:

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