Calculate the area of the following triangles, giving your answers to 2 decimal places:
(a) The right-angled triangle with sides a=16, b=63, and c=65.
(b) The triangle with angle α = 40° and adjacent sides b=10 and c=20.
do you want the answer or no. Weather you answer or not A squared + b squared = c squared this answers a
b squared - c squared = a squared
now for both of them you will have to use the square root of a and c squared. hope this helps :)
If you have a right-angled triangle, the area is
(1/2) base x height
You have the base and height, clearly 65 will not be used since it is the hypotenuse.
So go for it.
For the second, if you have two sides and the contained angle, then the area is
(1/2)(a)(b)sinØ, where a and b are the sides and Ø is the angle. You have all that, go for it.
Let me know what you get so I can check it
Sure! Let's calculate the area of each triangle step by step.
(a) Right-angled triangle with sides a=16, b=63, and c=65:
To calculate the area of a right-angled triangle, you can use the formula:
Area = (base * height) / 2.
In this case, we need to identify the base and height of the triangle. Since it is a right-angled triangle, we can consider a and b as the base and height, respectively. Let's plug in the values:
Area = (16 * 63) / 2
= 1008 / 2
= 504.
Therefore, the area of the right-angled triangle is 504 square units.
(b) Triangle with angle α = 40° and adjacent sides b=10 and c=20:
To calculate the area of a triangle, you can use the formula:
Area = (0.5 * base * height).
To use this formula, we first need to find the height of the triangle. Let's consider side b as the base, and side c as the hypotenuse (opposite the right angle). Since α = 40°, we need to find the height using trigonometric functions.
Using the sine function, we can find the height (h) as follows:
sin(40°) = h / 20.
Rearranging the equation, we get:
h = 20 * sin(40°).
Let's calculate the height:
h ≈ 20 * 0.64279
≈ 12.8558.
Now, we can calculate the area of the triangle:
Area = (0.5 * 10 * 12.8558)
= 64.2789.
Therefore, the area of the triangle is approximately 64.28 square units (rounded to 2 decimal places).