a What does the unknown angle tell you about what kind of triangle this is?
B
b The slanted sides are the hypotenuse of two congruent right triangles
C
c How can you use the tangent ratio to find the smaller of the unknown sides?
A
a ≈ 23.899 mm
B
b 66m
C
c ≈ 32.93inches
Practice makes perfect
a From the diagram, we see that this is a right triangle with a second angle of 45^(∘). If we call the unknown angle θ, we can by the Triangle Angle Sum Theorem write an equation.
When we know all sides of the triangle, we can find the perimeter.
7+7+sqrt(98) ≈ 23.899 mm
b Since this is a parallelogram, it must have opposite sides that are parallel and congruent.
By finding the length of one of the slanted sides, we can therefore determine the total perimeter. From the information in the given diagram, we can identify the legs of a right triangle.
When we know the length of the legs, we can use the Pythagorean Theorem to calculate the length of the slanted sides.
When we know the value of x, we can find the length of the smaller side
With this additional information, we can calculate the hypotenuse of the right triangle. Note that we will substitute the exact value of x, which is 4tan 60^(∘), to avoid rounding errors.
