Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

13. The SMHS Surveying Team decided to go on a vacation to a small island in the South Pacific.They chartered plane 2135 through the "Blue Ribbon Rent-A-Good Plane" Company. As the planeapproached the island, which was 1600 feet wide, the pilot, realizing that if you were on the SMHS surveying team that you were an excellent math student, announced that the angle of depression to the near side of the island was 25° and the angle of depression to the far side of the island was 22°. AT THAT VERY MOMENT the pilot realized that the plane was in DEEP TROUBLE and he must at that very instant know the altitude of the plane!!! The team, having studied under an exceptional math teacher, found the altitude of the plane and saved the day!!What was the plane's altitude?

13 The SMHS Surveying Team Decided To Go On A Vacation To A Small Island In The South PacificThey Chartered Plane 2135 Through The Blue Ribbon RentAGood Plane C class=

Sagot :

First, Lte's draw a picture of our problem:

which is equivalent to the following picture:

where h denotes the altitute and x is the horizontal distance from the near side of the island to the airplane.

Now, from triangle ACD, we have that

[tex]tan68=\frac{1600+x}{h}[/tex]

By distributing h, this last equation is equivalent to

[tex]tan68=\frac{1600}{h}+\frac{x}{h}\text{ ...\lparen A\rparen}[/tex]

Now, from triangle BCD,we have

[tex]tan65=\frac{x}{h}[/tex]

By substituting this result into equation (A), we have

[tex]tan68=\frac{1600}{h}+tan65[/tex]

Then, by moving tan65 to the left hand side, we get

[tex]tan68-tan65=\frac{1600}{h}[/tex]

or equivalently,

[tex]\frac{1600}{h}=tan68-tan65[/tex]

By taking reciprocals, we get

[tex]\frac{h}{1600}=\frac{1}{tan68-tan65}[/tex]

so, by moving 1600 to the right hand side, we get

[tex]h=\frac{1600}{tan68-tan65}[/tex]

which gives

[tex]h=\frac{1600}{2.47508-2.14450}[/tex]

Then, the altitude is given by

[tex]h=4839.9792\text{ ft}[/tex]

Therefore, by rounding to the nearest whole number, the answer is 4840 feet.

View image RoelV567993
View image RoelV567993
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.