5. a roof has an off - centre peak. the shorter side of the roof bc has a length of 13m. the base of the…

5. a roof has an off - centre peak. the shorter side of the roof bc has a length of 13m. the base of the roof measures 5m on the short side of the peak as indicated by dc and 9 metres on the longer side of the roof indicated by ad.\n a. determine the height of the roof, bd, rounded to the nearest whole number. (1/2)\n formula:\n calculations:\n solution with units:\n b. using the height of the roof determine the measure of angle a to the nearest degree. (2)\n formula:\n calculations:\n solution with units:\n financial services & personal budget\n 6. marc received a credit card statement that has an unpaid balance of $1128.32. the interest rate on this credit card is 20.1%. if this balance remains unpaid for 15 days how much simple interest will marc be charged after 15 days? (remember: 365 days/year) (1/2)\n formula:\n calculations:\n solution with units:

5. a roof has an off - centre peak. the shorter side of the roof bc has a length of 13m. the base of the roof measures 5m on the short side of the peak as indicated by dc and 9 metres on the longer side of the roof indicated by ad.\n a. determine the height of the roof, bd, rounded to the nearest whole number. (1/2)\n formula:\n calculations:\n solution with units:\n b. using the height of the roof determine the measure of angle a to the nearest degree. (2)\n formula:\n calculations:\n solution with units:\n financial services & personal budget\n 6. marc received a credit card statement that has an unpaid balance of $1128.32. the interest rate on this credit card is 20.1%. if this balance remains unpaid for 15 days how much simple interest will marc be charged after 15 days? (remember: 365 days/year) (1/2)\n formula:\n calculations:\n solution with units:

Answer

a. Determine the height of the roof (BD)

Explanation:

Step1: Apply Pythagorean theorem

Let (AB = 13m), (AD) be the base - half length and (BD) be the height. The base (AC) is composed of two parts, assume the base - half length (AD) (from the symmetry of the roof) and we know some side - length relationships. Using the Pythagorean theorem in right - triangle (ABD), (AB^{2}=AD^{2}+BD^{2}). Here, assume the base - half length (AD = 9m) and (AB = 13m). Then (BD=\sqrt{AB^{2}-AD^{2}}). [BD=\sqrt{13^{2}-9^{2}}=\sqrt{(13 + 9)(13 - 9)}=\sqrt{22\times4}=\sqrt{88}\approx 9m]

Answer:

(9m)

b. Determine the measure of angle (A)

Explanation:

Step1: Use the tangent function

In right - triangle (ABD), (\tan(A)=\frac{BD}{AD}). We know from part a that (BD\approx9m) and (AD = 9m). So (\tan(A)=\frac{9}{9}=1).

Step2: Find the angle

Since (\tan(A)=1), and (A) is an acute angle in a right - triangle, (A=\arctan(1)). Using the inverse - tangent function, (A = 45^{\circ}).

Answer:

(45^{\circ})

c. Calculate the simple interest

Explanation:

Step1: Recall the simple - interest formula

The simple - interest formula is (I=P\times r\times t), where (P) is the principal amount, (r) is the annual interest rate (in decimal form), and (t) is the time in years. Given (P = 1128.32), (r=0.201), and (t=\frac{15}{365}).

Step2: Substitute the values

[I = 1128.32\times0.201\times\frac{15}{365}] [I=1128.32\times0.201\times0.041096] [I\approx1128.32\times0.00826] [I\approx9.32]

Answer:

($9.32)