Question

 1.  A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? Explain.

 

 2.  A highway makes an angle of 6 with the horizontal. This angle is maintained for a horizontal distance of 5 miles.

To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance.
 3. A forest ranger spots a fire from a 28-foot tower. The angle of depression from the tower to the fire is 11 .
To the nearest foot, how far is the fire from the base of the tower? Show the steps

Answer 1

1.
pythagorean theorem: take the short sides and multiply the squares and compare to the square of the long side to know if the triangle is right, obtuse, acute. If the triangle is a right triangle then according to the pythagorean theorem the squares of the two shorter sides, added together, will equal the square of the hypotenuse.

10 squared (100) plus 7 squared (49) = 149

15 squared = 225

Therefore this triangle is not right. This is an acute triangle because the hypotenuse (is it still a hypotenuse if the triangle is not right?) is shorter than a right triangle's hypotenuse would be.

2. ?

3.we can find it by using tan law tanx= opposite/adj so let y -the distance of fire from the foot of tower x will be the angle x = 90-11 =79 so tan79=y/28 so y=28tan79 = 13.8789709291 or 13.88

Answer 2

thank you

Answer 3

anytime :)

Answer 4

 8.  Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. The vase had a height of 50 centimeters. Find the radius of the vase. Explain the method you would use to find the radius.

 


 9.  A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.

 

Answer 5

could u help with those to plz