Let’s say that you are biking on a road which is going down at angle of 15° for 2 km and then it levels off (no incline) for 2 km. Today she said to him, “Johnny you think that you are a good bike rider. ChallengeĬhallenge: Sara loves to tease her boyfriend Johnny. Johnny and Sara went through their Trig book and found several more identities and tried to prove them. Tommy, tell us what you decide and what your nephew thinks of his birthday present.

So the height of each ramp will be 7.8 cm because 60 x 0.13 = 7.8. I did not use the negative height because that would mean a ramp dug to go down into the ground. Sara: Here, we can also use the identity: sin (A/2) = ± √(1- cos A)/2.īecause, cos 15° = 0.966, sin A/2 will be 0.13. My brother who is Cody’s dad may decide that this is too risky and I should get the two ramps each with half of the angle 15°. That sounds perfect but I am going to let Cody’s dad decide. If you were to make the angle A equal to B, it would become: sin (2A) = 2 sin A cos A, Because for angle A which is 10°, sin A = 0.174 and cos A = 0.985, sin (2A) = 0.342 or the height of two 10° ramps which is a 20° incline would be 0.3428 x 60 cm which is approximately 20.6 cm which is a about 8 inches. Sara: You know that sin (A + B) = sin A cos B + cos A sin B. What height would it be if I just stacked two ramps each of angle A which is 10°. I am worried that 25.36 cm, which is almost ten inches, may be too high for Cody. Tommy: I see the height of the ramp B stacked on top of ramp A will be 60 x 0.4226 or 25.36 cm. Sara: One of the identities is: sin (A + B) = sin A cos B + cos A sin B So I will use one of the identities listed in our Trig book. The simplest way will be to get the value of sine of an angle from a calculator but Johnny here wants to learn some Trig. The hypotenuse will remain the same: 60 cm. Sara: If you stack a ramp of incline angle B on of top of a ramp of angle A, the total angle will be A + B. Stacking skate board ramps to get more height So this ramp would have a maximum height of 0.2588 x 60 or 15.53 cm. Tommy: I should be able to buy a 15° ramp. Sara: Just to show you that this relationship works. Tommy: I already gave you the measurements. You can also figure out cos A from this to be √(1 – 0.174 2) = 0.985, because sin 2 A + cos 2 A=1. With a hypotenuse of 60 cm, the height would be 0.174 x 60 cm or 10.44 cm. That means the height/hypotenuse = 0.174. Ramp A has an incline of 10° and a 60 cm long inclined surface. First, let us look at the individual ramps.

I don’t know what the height will be then. When he gets really good, I can stack and glue one ramp on top of the other to make a really high one. In the beginning, he could use these two ramps separately. I want another 60 cm ramp with a height of 15 cm. I saw a ramp with a 10° angle of inclination and the inclined surface on the top was 60 centimeter (cm). Tommy: If the ramp is very low, it will be no fun for him but if it is too high, he might hurt himself. He already has a helmet and he will have to wear it too. I bet he’ll have fun with them but they have to be small enough that he doesn’t hurt himself. I am thinking of buying a couple of small skate ramps for him. Tommy: You know Cody’s family lives in the country side and they have a long driveway. Johnny: So what are you planning? Tommy wanted to give Cody skate ramps He loved it and wanted to try but we didn’t let him because he is too young. He watched boys and girls go onto different types of launch ramps and quarter pikes. A month ago, we took him to a skate park. I want to do something bigger and more special than that. Johnny: Will you take him out for an ice-cream or something? I want to do something special for his birthday. I guess he not only likes me but also looks up to me. Whenever I go to their place, he gives me a big hug and then follows me around until I leave. Tommy: Yes, I really like the little rascal. The little tyke will be three this Sunday. Johnny and Sara were sitting in the school cafeteria when Tommy, a common friend of theirs, joined them.

Little tyke bike