Problem of the Day: 1/24/13

In the diagram below, angle B is 80 degrees more than angle D. What are the measures of each angle in the triangle?

Solution to yesterday’s problem:

We can solve this problem using the rate formula d=rt.

$1.49\times10^{11}=(2.99 \times10^8)t$

Now we just need to divide. To divide two numbers in scientific notation, just divide the decimal numbers and subtract the exponents. To find out why this works, I’ll write out the division problem without exponents:

$\frac{1.49\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10\times10}{2.99\times10\times10\times10\times10\times10\times10\times10\times10}$

The eight tens in the denominator cancel with eight tens from the numerator, leaving three tens in the numerator left over.

Dividing, we get $0.498\times10^3$. In this case, we should either convert it to scientific notation by moving the decimal place one to the right, or we should convert it to a number without scientific notation. In scientific notation we get $4.98\times10^2$; in normal notation we get 498 seconds, or 8 minutes and 18 seconds.