If sinB = 3/5, find the value of tanB *

Step-by-step explanation:

First, recall the right triangle trigonometry ratios.

We are looking for tangent, so we will use the last ratio.

We know that the sine of B is 3/5. Since sine is opposite over hypotenuse, the opposite is 3 and the hypotenuse is 5.

But, tangent needs opposite and adjacent.

We have to find the adjacent. This can be done using the Pythagorean Theorem, because these ratios are used with right triangles.

where a and b are the legs and c is the hypotenuse.

We know the hypotenuse is 5 and one of the legs is 3.

Solve the exponents.

Subtract 9 from both sides of the equation to isolate the variable.

b is being squared. The inverse of a square is the square root. Take the square root of both sides.

The adjacent side is 4.

Now we know the opposite (3) and adjacent (4). We can substitute these into the tangent ratio.

tan(θ)= opposite/adjacent

tan(B)=3/4

The tangent of B is 3/4

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²