Black diamond run

Taleah is skiing down a black diamond run. She begins skiing at the top of a ski trail whose elevation is about 8625 feet. The ski run ends toward the base of the mountain at 3800 feet. The horizontal distance between these two points is about 4775 feet. To the nearest tenth, determine the angle of elevation to the top of the ski run.

Correct answer:

A =  45.3 °

Step-by-step explanation:

$$\begin{gathered} a=8625\text{ ft } \\ b=3800\text{ ft } \\ x=4775\text{ ft } \\ y=a-b=8625-3800=4825\text{ ft } \\ \tan A={\displaystyle \frac{y}{x}} \\ {A}_1=\arctan ({\displaystyle \frac{y}{x}})=\arctan ({\displaystyle \frac{4825}{4775}})\doteq 0.7906\text{ rad } \\ A=A_1{\to }^{\circ }=A_1\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=0.7906\cdot {{\displaystyle \frac{180}{\pi }}}^{\circ }=45.3^{\circ }=45^{\circ }17^{\mathrm{\prime }}54\mathrm{"} \end{gathered}$$

Try another example

Related math problems and questions:

• Angles of elevation
  From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of
• Elevation angles
  From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
• Clouds
  From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
• Aircraft
  The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
• Isosceles triangle 8
  If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
• Depth angles
  At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
• Ratio iso triangle
  The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.
• Shooter
  The shooter fired at a target from a distance 11 m. The individual concentric circle of targets has radius increments of 1 cm (25 points) by 1 point. The shot was shifted by 8' (angle degree minutes). How many points should win his shot?
• Road drop
  On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
• Distance of points
  A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
• Isosceles triangle 10
  In an isosceles triangle, the equal sides are 2/3 of the length of the base. Determine the measure of the base angles.
• Mountain railway
  Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
• The Eiffel Tower
  The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
• The mast
  The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
• Bevel
  I have bevel in the ratio 1:6. What is the angle and how do I calculate it?
• Pyramid
  Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
• Sphere in cone
  A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele