1. You have been hired to survey a new national park area. You begin at Point A on the map. You had originally planned to build a bridge from Point 1 to Point B, but have found the ground at Point 1 is too unstable. So, you decided to build the bridge from Point A to Point B. You know the distance from Point A to Point 1 is 30m. Within the AB1 triangle the angle at Point B is 45°, and the angle at Point A is 20°. How long will the bridge need to be? 2. You scout the territory northwest of B for 62m. You determine you can build a flat trail here. This trail will end at point C. Using an imaginary line due north from B you find the angle from B to C is 22°. How far north is Point C from Point B? 3. There is a hill at Point C, and you climb it to get an idea of where to travel to next. You see the edge of a forest (Point D). You climb back down to the bottom of the hill (Point C) and walk to Point D. You track your distance and find you have travelled 98m. Using a tool you find the angle from Point D to the top of the hill at Point C is 34.5°. How far is it from Point D to the top of the hill? 4. There is a large mountain between Point D and Point E. There is no safe way around it or over it that makes sense, so a tunnel will have to be built. You know the distance from Point D to Point 2 is 132m and the distance from Point 2 to Point E is 145m. Using the D2E triangle the angle at Point 2 is 22.5°. How long will the tunnel need to be to connect Point D and Point E? A Ropes Adventure Name:___________ 5. You plan to create a small camp area with Points E, F and a Point 3 (not on map), so that the three points will form an isosceles triangle with the 3rd point being southeast of E and F. E and F are 21m apart. What could the lengths of the other part of the isosceles triangle? What would the angles of the triangle you created be? 6. The distance from Point F to Point G appears to be the furthest yet, plus you will need to navigate a lake. Based on your other calculations, you determine that the distance from Point G to Point C would be 76m. The distance from Point C to F (if you could go in a straight line) is 102m. Using the triangle GCF the angle at Point C is 56°. The distance across the lake is 1/3 of the distance from Point G to Point F. If you were to build a rope bridge across the lake, how long will the bridge be? 7. You are almost there. You have mapped out a beautiful journey through the park. The distance from Point G to the end is 156m. You decide you might create an alternate trail from Point F to the End for those that do not want to cross the lake or forest. Using the Triangle GF(End) the angle at Point F is 72°. What would the length of the trail that travelled directly from Point F to the End?
1. You have been hired to survey a new national park area. You
begin at Point A on the map. You had originally planned to build
a bridge from Point 1 to Point B, but have found the ground at
Point 1 is too unstable. So, you decided to build the bridge from
Point A to Point B. You know the distance from Point A to Point 1
is 30m. Within the AB1 triangle the angle at Point B is 45°, and
the angle at Point A is 20°.
How long will the bridge need to be?
2. You scout the territory northwest of B for 62m. You determine
you can build a flat trail here. This trail will end at point C. Using
an imaginary line due north from B you find the angle from B to
C is 22°.
How far north is Point C from Point B?
3. There is a hill at Point C, and you climb it to get an idea of where
to travel to next. You see the edge of a forest (Point D). You
climb back down to the bottom of the hill (Point C) and walk to
Point D. You track your distance and find you have travelled
98m. Using a tool you find the angle from Point D to the top of
the hill at Point C is 34.5°.
How far is it from Point D to the top of the hill?
4. There is a large mountain between Point D and Point E. There is
no safe way around it or over it that makes sense, so a tunnel
will have to be built. You know the distance from Point D to
Point 2 is 132m and the distance from Point 2 to Point E is 145m.
Using the D2E triangle the angle at Point 2 is 22.5°.
How long will the tunnel need to be to connect Point D and Point
E?
A Ropes Adventure Name:___________
5. You plan to create a small camp area with Points E, F and a
Point 3 (not on map), so that the three points will form an
isosceles triangle with the 3rd point being southeast of E and F.
E and F are 21m apart.
What could the lengths of the other part of the isosceles
triangle?
What would the angles of the triangle you created be?
6. The distance from Point F to Point G appears to be the furthest
yet, plus you will need to navigate a lake. Based on your other
calculations, you determine that the distance from Point G to
Point C would be 76m. The distance from Point C to F (if you
could go in a straight line) is 102m. Using the triangle GCF the
angle at Point C is 56°. The distance across the lake is 1/3 of the
distance from Point G to Point F.
If you were to build a rope bridge across the lake, how long will
the bridge be?
7. You are almost there. You have mapped out a beautiful journey
through the park. The distance from Point G to the end is 156m.
You decide you might create an alternate trail from Point F to
the End for those that do not want to cross the lake or forest.
Using the Triangle GF(End) the angle at Point F is 72°.
What would the length of the trail that travelled directly from
Point F to the End?
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