If sides A and B of a triangle have lengths of 5 and 6 respectively, and the angle between them is #(pi)/2#, then what is the area of the triangle?

Question

Madelyn Adams · Accepted Answer

#15"sq.unit"#.

#"The angle btwn. sides A and B, i.e.," /_(A,B)=pi/2#. So, if we consider the side #B# as Base, then side #A# becomes altitude on the base. Therefore, The Area of the #Delta=1/2xx"base"xx"altitude"# #=1/2*5*6=15"sq.unit"#.

Caroline Adams · Answer

undefined To find the area of the triangle given the lengths of two sides and the angle between them, we can use the formula for the area of a triangle:

$$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $$

In this case, sides A and B of the triangle are given as 5 and 6 units, respectively, and the angle between them is $ \frac{\pi}{2} $ radians.

First, let's determine the base and height of the triangle:

The base of the triangle can be taken as side A, which is 5 units.

The height of the triangle can be calculated using trigonometric functions. Since the angle between sides A and B is $ \frac{\pi}{2} $ radians, the height of the triangle is the length of side B.

Now, we can calculate the area of the triangle:

$$ \text{Area} = \frac{1}{2} \times 5 \times 6 $$

$$ \text{Area} = \frac{1}{2} \times 30 $$

$$ \text{Area} = 15 $$

Therefore, the area of the triangle is 15 square units.