Jeremy's car went 300 miles (highway) on 10 gallons of gasoline. What was the average number of miles per gallon?
2 answers:
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Length of segment of the hypotenuse adjacent to the shorter leg is 5 inches and the length of the altitude is 3 inches.
Step-by-step explanation:
Step 1: Let the triangle be ΔABC with right angle at B. The altitude drawn from B intersects the hypotenuse AC at D. So 2 new right angled triangles are formed, ΔADB and ΔCDB.
Step 2: According to a theorem in similarity of triangles, when an altitude is drawn from any angle to the hypotenuse of a right triangle, the 2 newly formed triangles are similar to each other as well as to the bigger right triangle. So ΔABC ~ ΔADB ~ ΔCDB.
Step 3: Identify the corresponding sides and form an equation based on proportion. Let the length of the altitude be x. Considering ΔABC and ΔADB, AB/DB = AC/AB
⇒ 6/x = 12/6
⇒ 6/x = 2
⇒ x = 3 inches
Step 4: To find length of the hypotenuse adjacent to the shorter leg (side AB of 6 inches), consider ΔADB.
⇒
⇒
⇒
⇒
⇒
⇒AD = 5 inches
Answer:
A. 49 feet
B. 66 feet (round to the nearest foot)
C. 4 seg
Step-by-step explanation:
A. What is the height of the ball after 3 seconds?
For
B. What is the maximum height of the ball? round to the nearest foot
then
For
C. When will the ball hit the ground?
The ball will hit the ground when
so,
Using the quadratic equation