Find the area of given ∆abc angle b=50degree and c=50 degree ,ac=5cm, BC=3cm?

Question

Answer

Area of triangle = 1/2 * b*h
and find it urself ...
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Answer

Answer

Given:
Angle B = 50 degrees
Angle C = 50 degrees
AC = 5 cm
BC = 3 cm

To Find:
Area of triangle ABC

Solution:
To find the area of triangle ABC, we can use the formula: Area = 1/2 * base * height.

Step 1: Finding the height of the triangle
The height of the triangle can be found by drawing a perpendicular from vertex A to BC. Let's call this point D.

Step 2: Finding the length of AD
As we have a right-angled triangle ABD, we can use trigonometric ratios to find the length of AD.
In triangle ABD,
Angle BAD = 90 degrees
Angle ABD = 50 degrees
Using the trigonometric ratio for the sine function, we can write:
sin(ABD) = AD / AB
sin(50) = AD / 3
AD = 3 * sin(50)

Step 3: Finding the length of BD
Using the property of a triangle that the sum of the angles is 180 degrees, we can find angle A as:
Angle A = 180 - Angle B - Angle C
Angle A = 180 - 50 - 50
Angle A = 80 degrees

In triangle ABD,
Angle ABD = 50 degrees
Angle ADB = 80 degrees
Using the trigonometric ratio for the sine function, we can write:
sin(ADB) = BD / AB
sin(80) = BD / 3
BD = 3 * sin(80)

Step 4: Finding the length of CD
CD = BC - BD
CD = 3 - BD

Step 5: Finding the area of triangle ABC
The area of triangle ABC can be found using the formula:
Area = 1/2 * base * height
Area = 1/2 * AC * CD

Now, substitute the values of AC and CD:
Area = 1/2 * 5 * (3 - BD)

Finally, substitute the values of BD from Step 3:
Area = 1/2 * 5 * (3 - 3 * sin(80))

Simplify the expression to find the area.

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