What is the angle, in radians, of arcsin(1/2)

1 answer:

6 0

$\frac{\pi}{6}$

When you are asked what is the sin of π/6, or 30 degrees, you would look at the special triangle (30-60-90) to see that sin, or opposite over hypotenuse, of π/6 is 1/2. Arcsin, or csc, will present you with the ratio, 1/2, and ask for the angle. It's essentially working the question backwards.

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Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Veronika [31]

Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

<u>Area of a Triangle:</u>

A triangle of base B and height H (both must be perpendicular) has an area of:

$\displaystyle A=\frac{BH}{2}$

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

$\displaystyle A=\frac{5*4}{2}=10$