Homeschool Math Blog

Someone (a student perhaps?) sent me this problem From a horizontal distance of 8.5km a pilot observes that the angle of depression of the top and base of a central tower are 30 degrees and 33 degrees respectively.  Calculate  a. the shortest distance between the pilot and the base of the central tower b. the height of the central tower. Actually, a good part of this problem is to draw the correct diagram. Once you have the image right, then the math should be fairly obvious. But I'm going to help you out! Here's the image for this situation: (not to scale) The solution is posted here .

Trigonometry: Finding the value of sine Pi/3. First we need to remember that the whole circle is 360° and in radians it is 2Pi. So then Pi is 180°, and Pi/3 is 60°. To find sine of Pi/3, you'd want to have a right triangle with one angle 60°. Fortunately that is easy to come by; just take an equilateral triangle and draw an altitude to it. You will have two identical 30°-60°-90° triangles. And yes this is one of the special triangles - also used in drafting, and there are rulers in this shape . Where on this picture is the 60° angle? Where's the 30° angle? Now, to get sine 60° one needs side lengths. I made the sides of this equilateral triangle ABC to be 2 units. The side CD is obviously just 1 unit (easy numbers thus far!) But what about the height h? Well, that's where we need to dig up the goold ole' Pythagoras. Can't forget him. You write the equation, h 2 + 1 2 = 2 2 h 2 = 2 2 − 1 2 = 3. So taking square roots... h = √3. Then, to the sine. Remember sine i...

I get lots of questions, seemingly, about sine. It's because one of my pages with that topic ranks well in search engines and has the comment box in the end. Here's another one: how to measure right triangle sine? Well, you don't measure the sine per se. You measure certain sides of the triangle, and then calculate the sine. For example, in this picture, if we want to find the sine of the angle α, we measure the opposite side and the hypotenuse. They are already given as 2.6 and 6 units. Then just take their ratio: 2.6/6 and that's your sin α. You might also enjoy reading my lesson about sine in a right triangle . Tags: math , trigonometry

Another (student?) question along trigonometry lines: Sketch the sinusodial waveform given below over one complete cycle showing all essential values. i = 25sin(2t-30degress). Use a graphic calculator or an online version, such as Function Flyer at Shodor.org . There are more online graphing resources at my site . You need to change the 30 degrees to radians first. So compare 30 to 360; 30/360 is same as 1/12. So take 1/12th part of 2π, which is π/6. Then enter the function. With the Shodor grapher, you need to use * for multiplication and x for variable, instead of t, and not use degrees but radians. Seeing the sine graph will surely help you sketch yours on paper. Obviously the highest value is 25, the minimum value is -25. To find its zeros, you need to think: When does sin y = 0???? It's when y = _______ or y = _______ or when y = ______ (there are tons of these of course since it's cyclical). Now take the argument 2t-π/6 and let it equal those numbers you found. 2t-π/...