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.
the area is just 1/2 ab
the area is just 1/2 bc sinα
To calculate the area of triangles, we can use different formulas depending on the information given. Let's go through each triangle and calculate their areas step by step.
(a) Right-angled triangle with sides a=16, b=63, and c=65:
We know that the area of a right-angled triangle is given by the formula:
Area = 1/2 * base * height.
In this case, we have the lengths of two sides, a and b, which are perpendicular to each other. Therefore, we can use either a or b as the base and the other as the height.
Let's choose side a=16 as the base and side b=63 as the height. Plugging in these values into the formula, we get:
Area = 1/2 * 16 * 63 = 504.
So, the area of this right-angled triangle is 504 square units.
(b) Triangle with angle α = 40° and adjacent sides b=10 and c=20:
To find the area of this triangle, we need to use the formula:
Area = 1/2 * b * c * sin(α).
Here, b and c are the lengths of the adjacent sides, and α is the angle between them.
Let's plug in the given values into the formula:
Area = 1/2 * 10 * 20 * sin(40°) = 100 * sin(40°).
To calculate sin(40°), we can use a scientific calculator or an online trigonometry calculator. The result is approximately 0.64279.
Now, we can calculate the area:
Area = 100 * 0.64279 = 64.279.
Therefore, the area of this triangle is 64.279 square units, rounded to 2 decimal places.
Remember, when working with triangles, it is essential to use the correct formulas and have accurate measurements in order to obtain accurate results.