d The area of a triangle is calculated by multiplying the base and height of the triangle and dividing the product by 2.
A
a x≈ 14sqrt(3)units
B
b x≈ 5.78 units
C
c Cannot exist, see solution.
D
d x=24units
Practice makes perfect
a From the diagram we see a right triangle. Since one of the non-right angles is 60^(∘), this is a 30-60-90 triangle. In such a triangle, the legs and hypotenuse have the following relationship.
The hypotenuse of our triangle is 28 units. With this information we can write and solve the following equation.
2a=28 ⇔ a= 14
Now we can determine the value of x.
x=asqrt(3) ⇒ x= 14sqrt(3)
b In this triangle we know two angles and the opposite side of one of them. To find the opposite side of the second angle, we can use the Law of Sines.
c In a right triangle the hypotenuse is always greater than either of its legs. From the diagram we see that this is not the case, which means this triangle cannot exist.
d The area of a triangle is calculated by multiplying the base and height of the triangle and dividing the product by 2. From the diagram, we see that the base is 8 units and the height is x units. With this information we can write the following equation.
A=1/2(8)(x)
The area of the triangle should equal 96 square units. Therefore, if we set the area equal to 96 we can solve for the triangle's height x.
