Question

how to solve this isosceles triangle when AB=AC =17.5cm and BC= 28cm calculate the area of the triangle of ABC

Answer 1

147 cm^2

Step-by-step explanation:

We can use two formulas either
`(1)/(2)`(b×h) but for this, we need a line that is perpendicular to the base and we do not have that. The next formula we can use is
`(1)/(2)`(product of two sides) × Sin(angle between the two sides). Luckily we have all three sides but no angle. To find the angle we can simply use the cosine law. Cosine law has two forms, one for finding the side and another for the angle (I'll attach it).

Cos A= (a^2+b^2-c^2) (the side opposite to the angle)/2ab

We can find any angle but I'll find angle A.

Plug in the values.

A= Cos^-1((17.5^2+17.5^2-28^2)/2(17.5)^2) When we have to find the angle, the cos we shift will turn into inverse but for the side, it will just become the denominator.

A= 106.26°

Now just use the formula
`(1)/(2)`(17.5)^2 × Sin(106.26)= 147 cm^2

Feel free to ask any doubts!

Answer 2

To find the area of the isosceles triangle ABC, first determine the height using the Pythagorean theorem, then apply the area formula (1/2 × base × height) to get 147 cm².

Step-by-step explanation:

To solve for the area of an isosceles triangle where sides AB = AC = 17.5 cm and base BC = 28 cm, you first need to find the height (h) of the triangle, which is the line segment from vertex A perpendicular to the base BC. Since the triangle is isosceles, the height will bisect the base, creating two right-angled triangles where the hypotenuse is 17.5 cm and one leg is half of BC, so one leg is 14 cm. Using the Pythagorean theorem, we can find the height (h = √(AB² - (BC/2)²)) which is the missing side of the right triangle.

Calculate the height as follows:

h = √(17.5² - 14²)

= √(306.25 - 196)

= √110.25

= 10.5 cm

Now, apply the formula for the area of a triangle (1/2 × base × height).

Area = 1/2 × 28 cm × 10.5 cm

= 14 cm × 10.5 cm

= 147 cm²

So, the area of triangle ABC is 147 cm².