244 Part 3: The Shape of the World
CHECK POINT- 'XYZ is a right triangle with right angle Y and hypotenuse XZ equal to 42
cm. If X measures 56r, find the length of side XY to the nearest centimeter. - 'ABC is a right triangle with right angle C, A = 46r, and side AC is 42 cm
long. Find the length of BC to the nearest centimeter. - In right 'RST, S is a right angle and RT = 24. If T measures 30r, find the
length of RS to the nearest centimeter. - In right 'ABC with right angle at C, B = 76r, and side BC is 80 feet. Find the
length of hypotenuse AB. - In right 'XYZ with right angle at Y, X = 32r, and side YZ is 58 cm. Find the
length of XY to the nearest centimeter.
The Least You Need to Know
- To find the area of irregular figures, find the area of the whole figure and subtract
the area of the unshaded portions, or divide the area into shapes whose areas can
be calculated and add the results. - When triangles are similar, corresponding sides are in proportion, and those
proportions can be used to find the lengths of unknown sides. - Trigonometric ratios, based on families of similar right triangles, can be used to
find unknown sides of right angles. - For any acute angle A in a right triangle,
sin(A) = length of the opposite side divided by the length of the hypotenuse,
cos(A) = length of the adjacent side divided by the length of the hypotenuse, and
tan(A) = length of the opposite side divided by the length of the adjacent side.